quasi-Newton approximation of Hessian of Lagrangian

[MaxenceGollier]

When we compute the Hessian of the Lagrangian in fact we compute the Hessian of the objective and the dual variables are discarded.
I think this should not be the case, there is no reason for not approximating the constraints with a quasi-Newton model...
IPOPT for example does compute each constraint as a quasi-Newton model when we use quasi-Newton approximations for the problem.

NLPModelsModifiers.jl/src/quasi-newton.jl

Lines 188 to 197 in c6befb7

	function NLPModels.hprod!(
	nlp::QuasiNewtonModel,
	x::AbstractVector,
	y::AbstractVector,
	v::AbstractVector,
	Hv::AbstractVector;
	kwargs...,
	)
	return hprod!(nlp, x, v, Hv; kwargs...)
	end

[MaxenceGollier]

Actually, to get the qN approximation of the Lagrangian, I should just push $$\nabla f_{k+1} + J_{k+1}^Ty_{k+1} - \nabla f_{k} - J_{k}^Ty_{k}$$ to update the approximation at each iterate instead of $$\nabla f_{k+1} - \nabla f_{k}$$ so this is irrelevant. I am closing this issue now.

[tmigot]

Actually, @MaxenceGollier if you have a relatively small example with this it could be the start of a good tutorial?